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Beliebt Rechnen >

derivative f(x)=x^{5/2}e^x

Lösung

ableitung von

f (x) = x^{\frac{5}{2}} e^{x}

Lösung

\frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{5}{2}} e^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{5}{2}}, g = e^{x}

= \frac{d}{d x} (x^{\frac{5}{2}}) e^{x} + \frac{d}{d x} (e^{x}) x^{\frac{5}{2}}

\frac{d}{d x} (x^{\frac{5}{2}}) = \frac{5 x ^{\frac{3}{2}}}{2}

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{5 x ^{\frac{3}{2}}}{2} e^{x} + e^{x} x^{\frac{5}{2}}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 e ^{x} x ^{\frac{3}{2}}}{2} + e^{x} x^{\frac{5}{2}}

Graph

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